weighted fused graphical lasso
Description
wfgl
estimates joint partial correlation matrices from two multivariate
normal distributed datasets using an ADMM based algorithm. Allows for paired data.
Usage
1 2 3 4 5  wfgl(D1, D2, lambda1, lambda2, paired = TRUE, automLambdas = TRUE,
sigmaEstimate = "CRmad", pairedEst = "Regbasedsim", maxiter = 30,
tol = 1e05, nsubset = 10000, weights = c(1,1), rho=1, rho.increment = 1,
triangleCorrection = TRUE, alphaTri = 0.01, temporalFolders = FALSE,
notOnlyLambda2 = TRUE)

Arguments
D1 
first population dataset in matrix n_1 \times p form. 
D2 
second population dataset in matrix n_2 \times p form. 
lambda1 
tuning parameter for sparsity in the precision matrices (sequence of lambda1 is allowed). 
lambda2 
tuning parameter for similarity between the precision matrices in the two populations (only one value allowed at a time). 
paired 
if 
automLambdas 
if 
sigmaEstimate 
robust method used to estimate the variance of estimated partial correlations: name that uniquely identifies

pairedEst 
type of estimator for the correlation of estimated partial correlation coefficients when 
maxiter 
maximum number of iterations for the ADMM algorithm. 
tol 
convergence tolerance 
nsubset 
maximum number of estimated partial correlation coefficients (chosen randomly) used to select 
weights 
weights for the two populations to find the inverse covariance matrices. 
rho 
regularization parameter used to compute matrix inverse by eigen value decomposition (default of 1). 
rho.increment 
default of 1. 
triangleCorrection 
if 
alphaTri 
significance level for the tested triangle graph structures. 
temporalFolders 
if 
notOnlyLambda2 
if 
Details
wfgl
uses a weightedfused graphical lasso maximum likelihood estimator by solving:
\hat{Ω}_{WFGL}^{λ} = \arg\max\limits_{Ω_X,Ω_Y} [∑_{k=X,Y} \log\detΩ_k tr(Ω_k S_k)  P_{λ_1,λ_2,V}(Ω_X,Ω_Y)],
with
P_{λ_1,λ_2, V}(Ω_X,Ω_Y) = λ_1Ω_X_1 + λ_1Ω_Y_1 +λ_2∑_{i,j} v_{ij} Ω_{Y_{ij}}Ω_{X_{ij}},
where λ_1 is the sparsity tuning parameter, λ_2 is the similarity tuning parameter, and V = [v_{ij}]
is a p\times p matrix to weight λ_2 for each coefficient of the differential precision matrix.
If datasets are independent (paired = "FALSE"
), then it is assumed that v_{ij} = 1 for all pairs (i,j).
Otherwise (paired = "TRUE"
), weights are estimated in order to account for the dependence structure between datasets in the differential
network estimation.
Lambdas can be estimated in each iteration by controlling the expected false positive rate (EFPR) in
case automLambdas = TRUE
. This transforms the problem of selecting the tuning parameters λ_1 and λ_2 to the
selection of the desired EFPR. In case lambda2
is a single value and lambda1
is a vector with several values, then lambda selection
approaches implemented at lambdaSelection
can also be used.
If triangleCorrection = TRUE
, the weakest edges of estimated triangular motifs are further tested. The reason is that edges that complete
triangular graph structures suffer an overestimation when applying the ADMM due to using regularized inverse procedures.
Value
An object of class wfgl
containing the following components:
path 
adjacency matrices. 
omega 
precision matrices. 
triangleCorrection 
determines if triangle structures are tested. 
weakTriangEdges 
weakest edges in triangle structures which have been tested. 
weakTriangEdgesPval 
pvalues for the weakest edge in triangle structures. 
diff_value 
convergence control. 
iters 
number of iterations used. 
corEst 
dependence structure estimated measure used in the estimation to account for dependent datasets. 
Author(s)
Caballe, Adria <a.caballe@sms.ed.ac.uk>, Natalia Bochkina and Claus Mayer.
References
Danaher, P., P. Wang, and D. Witten (2014). The joint graphical lasso for inverse covariance estimation across multiple classes. Journal of the Royal Statistical Society: Series B (Statistical Methodology) (2006), 120.
Boyd, S. (2010). Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers. Foundations and Trends in Machine Learning 3(1), 1122.
See Also
plot.wfgl
for graphical representation.
wfrl
for weighted fused regression lasso.
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 
# example to use of wfgl
EX2 < pcorSimulatorJoint(nobs =50, nclusters = 3, nnodesxcluster = c(30, 30,30),
pattern = "pow", diffType = "cluster", dataDepend = "diag",
low.strength = 0.5, sup.strength = 0.9, pdiff = 0.5, nhubs = 5,
degree.hubs = 20, nOtherEdges = 30, alpha = 2.3, plus = 0,
prob = 0.05, perturb.clust = 0.2, mu = 0, diagCCtype = "dicot",
diagNZ.strength = 0.6, mixProb = 0.5, probSign = 0.7,
exactZeroTh = 0.05)
## not run
#wfgl1 < wfgl(EX2$D1, EX2$D2, lambda1 = 0.05, lambda2 = 0.1, paired = TRUE,
# automLambdas = TRUE, sigmaEstimate = "CRmad", pairedEst = "Regbasedsim",
# maxiter = 30)
#print(wfgl1)
